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Infinitely many non-radial singular solutions of

Part of: Miscellaneous topics - Partial differential equations Partial differential equations Nonlinear dynamics Elliptic equations and systems

Published online by Cambridge University Press:  17 October 2017

Yasuhito Miyamoto
Yasuhito Miyamoto*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan ([email protected])
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Abstract

We construct countably infinitely many non-radial singular solutions of the problem

of the form

where v(σ) depends only on σ ∈𝕊N−1. To this end we construct countably infinitely many solutions of

using ordinary differential equation techniques.

Keywords

non-radial singular solutionsinfinitely many solutionsprescribed curvature equationphase-plane analysis

MSC classification

Secondary: 35J61: Semilinear elliptic equations 35R01: Partial differential equations on manifolds 70K05: Phase plane analysis, limit cycles 35B08: Entire solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 1 , February 2018 , pp. 133 - 147
Copyright
Copyright © Royal Society of Edinburgh 2018 

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